Bubble sort is a sorting algorithm that consists of a number of rounds. On each round the algorithm scans the array from left to right and swaps any adjacent elements that are in the wrong order.

Given an array of $n$ integers, calculate the number of bubble sort rounds needed to sort the array.

Input

The first line has an integer $n$: the array size.

The next line has $n$ integers $x_1,x_2,\dots,x_n$: the array contents.

Output

Print one integer: the number of rounds.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $1 \le x_i \le 10^9$

Example

Input:

5
3 2 4 1 4

Output:

3

Explanation: Bubble sort needs three rounds to sort this array. The array contents after each round are $[2,3,1,4,4]$, $[2,1,3,4,4]$, and $[1,2,3,4,4]$.